Linear Equation from Table of Values: Slope-Intercept Form

Math Problem Statement

Find the equation of the linear function represented by the table below in slope-intercept form.

The task in the image asks to find the equation of the linear function represented by the table in slope-intercept form ( $y = mx + b$ ).

\hline x & y \\ \hline 1 & -2 \\ 2 & 0 \\ 3 & 2 \\ 4 & 4 \\ \hline \end{array}$$ --- ### Step 1: Find the slope ($$m$$) The formula for slope is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using the points $$(1, -2)$$ and $$(2, 0)$$: $$m = \frac{0 - (-2)}{2 - 1} = \frac{2}{1} = 2$$ So, the slope is $$m = 2$$. --- ### Step 2: Find the $$y$$-intercept ($$b$$) The slope-intercept form is: $$y = mx + b$$ Substitute $$m = 2$$ and use any point from the table to find $$b$$. Let’s use the point $$(1, -2)$$: $$-2 = 2(1) + b$$ $$-2 = 2 + b$$ $$b = -4$$ --- ### Final Equation: $$y = 2x - 4$$ This is the equation of the linear function in slope-intercept form. --- Do you have any questions or would you like further clarification? Here are 5 related questions for practice: 1. How would the equation change if the slope was negative? 2. What is the slope if the table was modified to include a point $$(5, 6)$$? 3. How do you verify if a point lies on the line $$y = 2x - 4$$? 4. What is the equation of a line parallel to $$y = 2x - 4$$ but passing through $$(0, 3)$$? 5. What is the significance of the slope and $$y$$-intercept in real-world applications? **Tip:** When working with tables, always check if the slope is consistent between all pairs of points to confirm the relationship is linear!

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Linear Equations
Slope-Intercept Form
Coordinate Geometry

Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b

Concept of linearity and slope

Grades 8-10

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